One problem with this idea is the attached cartridge may or may not (more probable) be symmetrical and therefore balanced on the front to rear axis. So, it would be off from the second you mounted the cartridge.

Also, the stylus/cantilever mount may not be exactly perpendicular to the top of the head shell viewed from the front. It could be close, but this is why each and every cartridge, even those from the same manufacture and model have different alignment settings. Particularly for azimuth.

Great care to achieve parallelism between the cartridge mounting surface and the level mounting surface would be required. And since that level is going to get glued in, then that throws off the whole ball of wax.

Also, the cartridge mount surface would also need a significant degree of flatness. I believe they try to do this today, but it is seldom the case. These steps by a manufacturer will add costs quickly to the tonearm package. I checked my 3DR arm on a granite block of known flatness and a digital dial indicator. To achieve better flatness I used a file and wet or dry sandpaper to 1000 grit. Sonic improvements are 'hearable' doing this. You achieve better cartridge coupling to the tonearm and do not induce mechanical stress to the cartridge housing. Most of the material I removed was simply paint.

And finally, the bubble level would add a viscous mass to the tonearm that is unnecessary 99% of the time. Once the bubble begins to move it's going to take energy to stop and reverse direction just the same as the tonearm. At a different rate of the tone arm and a different modulation as well. I would think at some frequencies, it would muddy the heck out of them!

AMG and Graham put a bubble level near the pivot. But, as noted by others, I'm not sure that this will have enough sensitivity. Perhaps those who have experience with these arms could weigh in. May be these bubble levels have a special liquid, or something. I'd imagine a light liquid might be more sensitive than a heavy oil.

Or attach a bubble level off the counterweight. Again, I'm not sure this will work, because of the sensitivity of bubble levels. My previous arm (a linear tracker) needed to be leveled very carefully and the manufacturer supplied a bubble level. It was utterly useless.

I do feel, though, that VTA is important. For me, when I get the VTA just right, the difference in the sound is.... astounding.

I was going to bring up the Graham and other high end tonearms but I'm glad someone beat me to it. I used a small bubble level on the headshell (well actually it sat flat on the cartridge top) on my terminator T-3. This was really easy to use as when the bubble read level, the top surface to the Jubilee was in fact level with the record surface; easily seen with one of those Millennium blocks. It was easy to estimate where you deviated from level from where the bubble was located. Just measured once and jotted down a few notes. I liked it as it actually sat in the large hole the Tomahawk tonearm had right over the cartridge. I liked it. Just make sure you set your tracking weight with it installed.